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  <h1>Source code for cdt.causality.pairwise.IGCI</h1><div class="highlight"><pre>
<span></span><span class="sd">&quot;&quot;&quot;Information Geometric Causal Inference (IGCI) model.</span>

<span class="sd">P. Daniušis, D. Janzing, J. Mooij, J. Zscheischler, B. Steudel,</span>
<span class="sd">K. Zhang, B. Schölkopf:  Inferring deterministic causal relations.</span>
<span class="sd">Proceedings of the 26th Annual Conference on Uncertainty in Artificial  Intelligence (UAI-2010).</span>
<span class="sd">http://event.cwi.nl/uai2010/papers/UAI2010_0121.pdf</span>

<span class="sd">Adapted by Diviyan Kalainathan</span>

<span class="sd">.. MIT License</span>
<span class="sd">..</span>
<span class="sd">.. Copyright (c) 2018 Diviyan Kalainathan</span>
<span class="sd">..</span>
<span class="sd">.. Permission is hereby granted, free of charge, to any person obtaining a copy</span>
<span class="sd">.. of this software and associated documentation files (the &quot;Software&quot;), to deal</span>
<span class="sd">.. in the Software without restriction, including without limitation the rights</span>
<span class="sd">.. to use, copy, modify, merge, publish, distribute, sublicense, and/or sell</span>
<span class="sd">.. copies of the Software, and to permit persons to whom the Software is</span>
<span class="sd">.. furnished to do so, subject to the following conditions:</span>
<span class="sd">..</span>
<span class="sd">.. The above copyright notice and this permission notice shall be included in all</span>
<span class="sd">.. copies or substantial portions of the Software.</span>
<span class="sd">..</span>
<span class="sd">.. THE SOFTWARE IS PROVIDED &quot;AS IS&quot;, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR</span>
<span class="sd">.. IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,</span>
<span class="sd">.. FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE</span>
<span class="sd">.. AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER</span>
<span class="sd">.. LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,</span>
<span class="sd">.. OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE</span>
<span class="sd">.. SOFTWARE.</span>
<span class="sd">&quot;&quot;&quot;</span>

<span class="kn">from</span> <span class="nn">.model</span> <span class="kn">import</span> <span class="n">PairwiseModel</span>
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="p">(</span><span class="n">MinMaxScaler</span><span class="p">,</span> <span class="n">StandardScaler</span><span class="p">)</span>
<span class="kn">from</span> <span class="nn">scipy.special</span> <span class="kn">import</span> <span class="n">psi</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>

<span class="n">min_max_scale</span> <span class="o">=</span> <span class="n">MinMaxScaler</span><span class="p">()</span>
<span class="n">standard_scale</span> <span class="o">=</span> <span class="n">StandardScaler</span><span class="p">()</span>


<span class="k">def</span> <span class="nf">eval_entropy</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;Evaluate the entropy of the input variable.</span>

<span class="sd">    :param x: input variable 1D</span>
<span class="sd">    :return: entropy of x</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="n">hx</span> <span class="o">=</span> <span class="mf">0.</span>
    <span class="n">sx</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
    <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">sx</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">sx</span><span class="p">[</span><span class="mi">1</span><span class="p">:]):</span>
        <span class="n">delta</span> <span class="o">=</span> <span class="n">j</span><span class="o">-</span><span class="n">i</span>
        <span class="k">if</span> <span class="nb">bool</span><span class="p">(</span><span class="n">delta</span><span class="p">):</span>
            <span class="n">hx</span> <span class="o">+=</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">delta</span><span class="p">))</span>
    <span class="n">hx</span> <span class="o">=</span> <span class="n">hx</span> <span class="o">/</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="n">psi</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">))</span> <span class="o">-</span> <span class="n">psi</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>

    <span class="k">return</span> <span class="n">hx</span>


<span class="k">def</span> <span class="nf">integral_approx_estimator</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;Integral approximation estimator for causal inference.</span>

<span class="sd">    :param x: input variable x 1D</span>
<span class="sd">    :param y: input variable y 1D</span>
<span class="sd">    :return: Return value of the IGCI model &gt;0 if x-&gt;y otherwise if return &lt;0</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">)</span>
    <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
    <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
    <span class="n">idx</span><span class="p">,</span> <span class="n">idy</span> <span class="o">=</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">argsort</span><span class="p">(</span><span class="n">x</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">argsort</span><span class="p">(</span><span class="n">y</span><span class="p">))</span>

    <span class="k">for</span> <span class="n">x1</span><span class="p">,</span> <span class="n">x2</span><span class="p">,</span> <span class="n">y1</span><span class="p">,</span> <span class="n">y2</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">x</span><span class="p">[[</span><span class="n">idx</span><span class="p">]][:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">x</span><span class="p">[[</span><span class="n">idx</span><span class="p">]][</span><span class="mi">1</span><span class="p">:],</span> <span class="n">y</span><span class="p">[[</span><span class="n">idx</span><span class="p">]][:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">y</span><span class="p">[[</span><span class="n">idx</span><span class="p">]][</span><span class="mi">1</span><span class="p">:]):</span>
        <span class="k">if</span> <span class="n">x1</span> <span class="o">!=</span> <span class="n">x2</span> <span class="ow">and</span> <span class="n">y1</span> <span class="o">!=</span> <span class="n">y2</span><span class="p">:</span>
            <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">((</span><span class="n">y2</span> <span class="o">-</span> <span class="n">y1</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span><span class="p">)))</span>

    <span class="k">for</span> <span class="n">x1</span><span class="p">,</span> <span class="n">x2</span><span class="p">,</span> <span class="n">y1</span><span class="p">,</span> <span class="n">y2</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">x</span><span class="p">[[</span><span class="n">idy</span><span class="p">]][:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">x</span><span class="p">[[</span><span class="n">idy</span><span class="p">]][</span><span class="mi">1</span><span class="p">:],</span> <span class="n">y</span><span class="p">[[</span><span class="n">idy</span><span class="p">]][:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">y</span><span class="p">[[</span><span class="n">idy</span><span class="p">]][</span><span class="mi">1</span><span class="p">:]):</span>
        <span class="k">if</span> <span class="n">x1</span> <span class="o">!=</span> <span class="n">x2</span> <span class="ow">and</span> <span class="n">y1</span> <span class="o">!=</span> <span class="n">y2</span><span class="p">:</span>
            <span class="n">b</span> <span class="o">=</span> <span class="n">b</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">((</span><span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">y2</span> <span class="o">-</span> <span class="n">y1</span><span class="p">)))</span>

    <span class="k">return</span> <span class="p">(</span><span class="n">a</span> <span class="o">-</span> <span class="n">b</span><span class="p">)</span><span class="o">/</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>


<div class="viewcode-block" id="IGCI"><a class="viewcode-back" href="../../../../causality.html#cdt.causality.pairwise.IGCI">[docs]</a><span class="k">class</span> <span class="nc">IGCI</span><span class="p">(</span><span class="n">PairwiseModel</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;IGCI model.</span>

<span class="sd">    **Description:** Information Geometric Causal Inference is a pairwise causal</span>
<span class="sd">    discovery model model considering the case of minimal noise :math:`Y=f(X)`,</span>
<span class="sd">    with :math:`f` invertible and leverages assymetries to predict causal</span>
<span class="sd">    directions.</span>

<span class="sd">    **Data Type:** Continuous</span>

<span class="sd">    **Assumptions:** Only the case of invertible functions only is considered, as the</span>
<span class="sd">    prediction would be trivial otherwise if the noise is minimal.</span>

<span class="sd">    .. note::</span>
<span class="sd">       P. Daniušis, D. Janzing, J. Mooij, J. Zscheischler, B. Steudel,</span>
<span class="sd">       K. Zhang, B. Schölkopf:  Inferring deterministic causal relations.</span>
<span class="sd">       Proceedings of the 26th Annual Conference on Uncertainty in Artificial  Intelligence (UAI-2010).</span>
<span class="sd">       http://event.cwi.nl/uai2010/papers/UAI2010_0121.pdf</span>

<span class="sd">    Example:</span>
<span class="sd">        &gt;&gt;&gt; from cdt.causality.pairwise import IGCI</span>
<span class="sd">        &gt;&gt;&gt; import networkx as nx</span>
<span class="sd">        &gt;&gt;&gt; import matplotlib.pyplot as plt</span>
<span class="sd">        &gt;&gt;&gt; from cdt.data import load_dataset</span>
<span class="sd">        &gt;&gt;&gt; data, labels = load_dataset(&#39;tuebingen&#39;)</span>
<span class="sd">        &gt;&gt;&gt; obj = IGCI()</span>
<span class="sd">        &gt;&gt;&gt;</span>
<span class="sd">        &gt;&gt;&gt; # This example uses the predict() method</span>
<span class="sd">        &gt;&gt;&gt; output = obj.predict(data)</span>
<span class="sd">        &gt;&gt;&gt;</span>
<span class="sd">        &gt;&gt;&gt; # This example uses the orient_graph() method. The dataset used</span>
<span class="sd">        &gt;&gt;&gt; # can be loaded using the cdt.data module</span>
<span class="sd">        &gt;&gt;&gt; data, graph = load_dataset(&quot;sachs&quot;)</span>
<span class="sd">        &gt;&gt;&gt; output = obj.orient_graph(data, nx.Graph(graph))</span>
<span class="sd">        &gt;&gt;&gt;</span>
<span class="sd">        &gt;&gt;&gt; #To view the directed graph run the following command</span>
<span class="sd">        &gt;&gt;&gt; nx.draw_networkx(output, font_size=8)</span>
<span class="sd">        &gt;&gt;&gt; plt.show()</span>
<span class="sd">    &quot;&quot;&quot;</span>

    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="sd">&quot;&quot;&quot;.Initialize the IGCI model.&quot;&quot;&quot;</span>
        <span class="nb">super</span><span class="p">(</span><span class="n">IGCI</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>

<div class="viewcode-block" id="IGCI.predict_proba"><a class="viewcode-back" href="../../../../causality.html#cdt.causality.pairwise.IGCI.predict_proba">[docs]</a>    <span class="k">def</span> <span class="nf">predict_proba</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">dataset</span><span class="p">,</span> <span class="n">ref_measure</span><span class="o">=</span><span class="s1">&#39;gaussian&#39;</span><span class="p">,</span>
                      <span class="n">estimator</span><span class="o">=</span><span class="s1">&#39;entropy&#39;</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
        <span class="sd">&quot;&quot;&quot;Evaluate a pair using the IGCI model.</span>

<span class="sd">        Args:</span>
<span class="sd">            dataset (tuple): Couple of np.ndarray variables to classify</span>
<span class="sd">            refMeasure (str): Scaling method (gaussian (default),</span>
<span class="sd">               integral or None)</span>
<span class="sd">            estimator (str): method used to evaluate the pairs (entropy (default)</span>
<span class="sd">               or integral)}</span>

<span class="sd">        Returns:</span>
<span class="sd">            float: value of the IGCI model &gt;0 if a-&gt;b otherwise if return &lt;0</span>
<span class="sd">        &quot;&quot;&quot;</span>
        <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="n">dataset</span>
        <span class="n">estimators</span> <span class="o">=</span> <span class="p">{</span><span class="s1">&#39;entropy&#39;</span><span class="p">:</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">:</span> <span class="n">eval_entropy</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">-</span> <span class="n">eval_entropy</span><span class="p">(</span><span class="n">y</span><span class="p">),</span> <span class="s1">&#39;integral&#39;</span><span class="p">:</span> <span class="n">integral_approx_estimator</span><span class="p">}</span>
        <span class="n">ref_measures</span> <span class="o">=</span> <span class="p">{</span><span class="s1">&#39;gaussian&#39;</span><span class="p">:</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">standard_scale</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)))</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span>
                        <span class="s1">&#39;uniform&#39;</span><span class="p">:</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">min_max_scale</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)))</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="s1">&#39;None&#39;</span><span class="p">:</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">x</span><span class="p">}</span>

        <span class="n">ref_measure</span> <span class="o">=</span> <span class="n">ref_measures</span><span class="p">[</span><span class="n">ref_measure</span><span class="p">]</span>
        <span class="n">_estimator</span> <span class="o">=</span> <span class="n">estimators</span><span class="p">[</span><span class="n">estimator</span><span class="p">]</span>

        <span class="n">a</span> <span class="o">=</span> <span class="n">ref_measure</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
        <span class="n">b</span> <span class="o">=</span> <span class="n">ref_measure</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>

        <span class="k">return</span> <span class="n">_estimator</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span></div></div>
</pre></div>

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